Supercooled Water - More on Icing

This question is a question on physcial phenomena, NOT on regulation (so
I am starting a new thread).

As I understand it, icing happens between +2C and -10C. Assuming this
is correct, I have three questions.

(a) Does that mean one is relatively safe if the surface temperature is
below -10C (and there is no temperature inversion, meaning that the
temperature is known to decrease as one goes up in altitude)?

(b) Is icing from 0C to +2C a possibility only when your aircraft skin
is colder than 0C (probably because you are descending from altitude)?
Or is there some other condition where this is possible?

(c) I have been told that icing is possible from -10C to 0C because
water sometimes get "super-cooled" (which I assume means that water gets
below freezing, but does not form ice for some reason). Is that right?
If so, under what atmospheric conditions does water get super-cooled?